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Natural Deduction for Quantum Logic

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Abstract

This paper presents a natural deduction system for orthomodular quantum logic. The system is shown to be provably equivalent to Nishimura’s quantum sequent calculus. Through the Curry–Howard isomorphism, quantum \(\lambda \)-calculus is also introduced for which strong normalization property is established.

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Notes

  1. We are using slightly different symbols and names than those used in [13].

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  1. Department of Information Engineering, National Institute of Technology, Oita College, 1666 Maki , Oita, 870-0152, Japan

    K. Tokuo

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  1. K. Tokuo
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Tokuo, K. Natural Deduction for Quantum Logic. Log. Univers. 16, 469–497 (2022). https://doi.org/10.1007/s11787-022-00307-7

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